''The hope, of course, is that we would sell their flights first,'' the agent says. ''Why not? It's their system.''

The federal government, however, can think of several reasons why not. Concerned that bias in reservation systems is crunching small airlines and keeping consumers from finding the best flight for their needs, the Civil Aeronautics Board (CAB) announced this week that it intends to regulate the systems.

''This is the single most important factor affecting competition in the airline industry today,'' says Daniel McKinnon, CAB chairman.

Under fire are the reservations systems run by three big airlines: American's SABRE, United's APOLLO, and TWA's PARS. These computerized data bases, which all list flights, price, and availability from many airlines, are provided to travel agents as a marketing service.

When you make a reservation at an agency that uses computers, it's likely you choose from a menu of flights provided by one of these three services. They account for 80 percent of the computers used by travel agents.

And the profit picture of many airlines depends on sales made through SABRE, APOLLO, and PARS. The CAB estimates that 40 to 60 percent of all plane tickets are sold by computer-equipped travel agencies.

But do these big data bases give prospective passengers a fair shake? American, United, and TWA all freely admit they try to make their own flights look best on the computer. Though listing order is determined by a variety of factors, including time of departure and length of flight, the host airline's planes are often first - and a CAB report says 70 percent of bookings are made from the first five or six flights flashed on the travel agent's screen.

''SABRE is a competitive marketing tool'' that cost $160 million to build, replies Gene Overbeck, an American Airlines senior vice-president. ''Display preference is critical. We are not prepared to give that up - though we may be prepared to alter it.''

Critics complain this means travel agents might not bother to look up flights that may better meet passenger's needs. And the reservations systems are so large, critics say, that their inherent bias is an unfair restraint of trade.

Small airlines say their schedule changes often aren't listed quickly, and that the price they pay to be listed has jumped 400 percent in two years. Frontier Airlines claims such harassment has cut business in Denver, its headquarters. A Braniff official has charged American's manipulation of SABRE helped cause Braniff's bankruptcy.

Frontier suggests that airlines owners of computer reservation systems should be required to form separate subsidiaries to handle the computerized reservations. These subsidiaries would have to treat all airlines equally.

The Department of Justice is investigating whether these reservation data bases violate antitrust law. And on Aug. 10, CAB took the first step toward regulation, asking airlines to submit internal documents on use of APOLLO, SABRE , PARS, and a few other small systems.